A multifocus optical vortex metalens, with enhanced signal-to-noise ratio, is presented, which focuses three longitudinal vortices with distinct topological charges at different focal planes. The design largely extends the flexibility of tuning the number of vortices and their focal positions for circularly polarized light in a compact device, which provides the convenience for the nanomanipulation of optical vortices.

The spin Hall effect (SHE) of light, as an analogue of the SHE in electronic systems, is a promising candidate for investigating the SHE in semiconductor spintronics/valleytronics, high-energy physics and condensed matter physics, owing to their similar topological nature in the spin-orbit interaction. The SHE of light exhibits unique potential for exploring the physical properties of nanostructures, such as determining the optical thickness, and the material properties of metallic and magnetic thin films and even atomically thin two-dimensional materials. More importantly, it opens a possible pathway for controlling the spin states of photons and developing next-generation photonic spin Hall devices as a fundamental constituent of the emerging spinoptics. In this review, based on the viewpoint of the geometric phase gradient, we give a detailed presentation of the recent advances in the SHE of light and its applications in precision metrology and future spin-based photonics.

The spin Hall effect (SHE) of light is a useful metrological tool for characterizing the structure parameters variations of nanostructure. In this letter we propose using the SHE of light to identify the graphene layers. This technique is based on the mechanism that the transverse displacements in SHE of light are sensitive to the variations of graphene layer numbers.Comment: 4 pages, 4 figure

The photonic spin Hall effect (SHE) in the reflection and refraction at an interface is very weak because of the weak spin-orbit interaction. Here, we report the observation of a giant photonic SHE in a dielectric-based metamaterial. The metamaterial is structured to create a coordinate-dependent, geometric Pancharatnam-Berry phase that results in an SHE with a spin-dependent splitting in momentum space. It is unlike the SHE that occurs in real space in the reflection and refraction at an interface, which results from the momentum-dependent gradient of the geometric Rytov-Vladimirskii-Berry phase. We theorize a unified description of the photonic SHE based on the two types of geometric phase gradient, and we experimentally measure the giant spin-dependent shift of the beam centroid produced by the metamaterial at a visible wavelength. Our results suggest that the structured metamaterial offers a potential method of manipulating spin-polarized photons and the orbital angular momentum of light and thus enables applications in spin-controlled nanophotonics. Keywords: geometric phase; metamaterial; photonic spin Hall effect INTRODUCTION Metamaterials or metasurfaces are artificial materials that are engineered to produce nearly any imaginable optical properties that are not found in nature. 1,2 They are typically structured at the subwavelength scale with ultrathin metallic or dielectric micro/nanoparticles or with holes opened in metallic films. Metamaterials exhibit unprecedented degrees of freedom in the polarization and phase manipulation of light via the geometric structuring of their structural units, especially on the wavelength scale, 3-9 which leads to applications such as vortex beam generators, 3,7 metalenses 10,11 and optical holography. 12,13 These materials also offer considerable potential for the manipulation of the angular moment of light and the photonic spin Hall effect (SHE), thereby providing convenient opportunities for spin-polarized photonics and nanophotonics. [14][15][16][17] The photonic SHE describes the mutual influence of the photon spin (polarization) and the trajectory (orbital angular momentum) of light-beam propagation, i.e., the spin-orbit interaction (SOI), which results in two types of geometric phases: the Rytov-VladimirskiiBerry (RVB) phase and the Pancharatnam-Berry (PB) phase. [18][19][20][21][22] The RVB phase is associated with the evolution of the propagation direction of light. When a light beam reflects/refracts at a planar interface between different media, a SOI occurs, and the corresponding momentum-dependent RVB phase leads to a spin-dependent real-

The spin Hall effect (SHE) of light in layered nanostructures is investigated theoretically in this paper. A general propagation model describing the spin-dependent transverse splitting of wave packets in the SHE of light is established from the viewpoint of classical electrodynamics. We show that the transverse displacement of the wave-packet centroid can be tuned to either a negative or a positive value, or even zero, by just adjusting the structure parameters, suggesting that the SHE of light in layered nanostructures can be enhanced or suppressed in a desired way. The inherent physics behind this interesting phenomenon is attributed to the optical Fabry-Perot resonance. We believe that these findings will open the possibility for developing new nanophotonic devices.

In this work, we develop a hybrid-order Poincaré sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincaré sphere and high-order Poincaré sphere to a more general form. Polarization evolution in inhomogeneous anisotropic media with special geometry can be conveniently described by state evolution along the longitude line on the hybrid-order Poincaré sphere. Similar to that in previously proposed Poincaré spheres, the Berry curvature can be regarded as an effective magnetic field with monopole centered at the origin of sphere and the Berry connection can be interpreted as the vector potential. Both the Berry curvature and the Pancharatnam-Berry phase on the hybrid-order Poincaré sphere are demonstrated to be proportional to the variation of total angular momentum. Our scheme provides a convenient method to describe the spin-orbit interaction in inhomogeneous anisotropic media.

We propose and experimentally demonstrate a novel interferometric approach to generate arbitrary cylindrical vector beams on the higher order Poincaré sphere. Our scheme is implemented by collinear superposition of two orthogonal circular polarizations with opposite topological charges. By modifying the amplitude and phase factors of the two beams, respectively, any desired vector beams on the higher order Poincaré sphere with high tunability can be acquired. Our research provides a convenient way to evolve the polarization states in any path on the high order Poincaré sphere.c 2014 Optical Society of America OCIS codes: (260.2110) Electromagnetic optics; (260.5430) Polarization.Light beam with spatially inhomogeneous state of polarization, also referred to as vector beam, has been investigated for many years due to its unique properties [1]. Comparing with the conventional homogeneous polarization represented by fundamental Poincaré sphere, the cylindrical vector beams can be represented by higher order Poincaré sphere (HOPS) [2][3][4]. Particular interests and investigations focused on the vector beams with radial and azimuthal polarizations, which can be represented as two points on the equator of the first-order Poincaré sphere. Such beams can be generated by twisted nematic liquid crystal [5][6][7], inserting phase elements in the laser resonator [8], computer-generated subwavelength dielectric gratings [9, 10], a conical Brewster prism [11], spatially variable retardation plates [12], and a binary phase mask [13]. The vector beams with special polarization symmetry can give rise to uniquely high-numericalaperture focusing properties that may find important applications in nanoscale optical imaging and manipulation [14][15][16][17][18][19].In this Letter, a novel interferometric method is proposed and experimentally demonstrated to generate arbitrary cylindrical vector beams on the HOPS. Homogeneous polarization on the fundamental Poincaré sphere can be seen as the superposition of two orthogonal circular polarizations corresponding to the two poles of the Poincaré sphere. Similarly, vector beams on the HOPS can be regarded as the linear superposition of two orthogonal circular polarizations with opposite topological charges. For homogenous polarization, two quarter-wave plates (QWPs) and one half-wave plate (HWP) with adjustable optical axis angles can transform it to any point on the fundamental Poincaré sphere [2]. For the HOPS, we use a modified Mach-Zender interferometer with which the amplitude and phase factors in each arm can be modified, respectively.In the parameter space of the HOPS, the state of polarization ψ ℓ can be represented by [3] Here, φ is the azimuthal angle and υ the polar angle in the spherical coordinate, respectively. L ℓ and R ℓ are orthogonal circular polarization vortexes with L ℓ = (x + iŷ)e −iℓϕ / √ 2 and R ℓ = (x − iŷ)e iℓϕ / √ 2, possessing spin angular momentum σ (σ = ±1) per photon where is the Plank constant. The factor e iℓϕ is the vortex phase associated with the orb...

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